GTPS Curriculum 5 th Grade Math. Topic: Topic 1- Place Value

Transcription

1 8 days / September Understand the place value system. 5.NBT.1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. 5.NBT.3. Read, write, and compare decimals to thousandths. 3a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). 3b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Topic: Topic 1- Place Value /Enduring How are whole numbers and decimals written, compared, and ordered? Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. Numbers can be used to tell how many. Place value can be used to compare and order whole numbers and decimals. 1.1 Place Value 1.2 Tenths and Hundredths 1.3 Thousandths 1.4 Decimal Place Value 1.5 Comparing and Ordering Decimal 1.6 Look for a Pattern Daily Quick check Masters

2 Suggested Blocks of Instruction: 10 days / September / October Understand the place value system. 5.NBT.4. Use place value understanding to round decimals to any place. Perform operations with multidigit whole numbers and with decimals to hundredths. 5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Topic: Topic 2-Adding & Subtraction Decimals /Enduring How can sums and differences of decimals be estimated? What are the standard procedures for adding and subtracting whole numbers and decimals? There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers so the calculation is easy to do mentally. Models and algorithms for adding or subtracting multi-digit decimals are just an extension of models and algorithms for adding or subtracting multi-digit whole numbers. Adding or subtracting multi-digit decimals is similar to adding or subtracting multi-digit whole numbers. A number line can be used to round whole numbers and decimals by making it easy to see which multiple of 10, 100, etc., or of 0.1, 0.01, etc., a number is closest to. There is more than one way to estimate a sum or difference. Each estimation technique gives one way to estimate by replacing numbers with other numbers that are close and easy to compute with mentally. Some sequences of numbers or objects repeat or grow in predictable ways. 2.1 Mental Math 2.2 Rounding Whole Numbers & Decimals 2.3 Estimating Sums & Differences 2.4 Modeling Addition & Subtraction Decimals 2.5 Problem Solving 2.6 Adding Decimals 2.7 Subtracting Decimals 2.8 Multiple-Step Problems

3 11 days /October Understand the place value system. 5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5. Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and twodigit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Topic: Topic 3-Multiplying Whole Numbers /Enduring What are the standard procedures for estimating and multiplying whole numbers? The properties of multiplication can be used to simplify computation and to verify mental math and paper and pencil algorithms. Basic facts and place-value patterns can be used to find products when one factor is a multiple of 10 or a multiple of 100. There is more than one way to estimate a product. Each estimation technique gives one way to estimate by replacing numbers with other numbers that are close and easy to compute with mentally. Some numbers can be represented using a base number and an exponent. The standard multiplication algorithm breaks the calculation into simpler calculations using place values starting with the ones, then the tens, and so on. 3.1 Multiplication Properties 3.2 Using Mental Math to Multiply 3.3 Estimating Products 3.4 Exponents 3.5 Distributive Property 3.6 Multiplying by 1-Digit Numbers 3.7 Multiplying by 2-Digit Numbers 3.8 Multiplying Greater Numbers 3.9 Draw a Picture and Write an Equation

4 Suggested Blocks of Instruction: 9 days /October / November Perform operations with multidigit whole numbers and with decimals to hundredths. 5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Topic: Topic 4-Dividing by 1-Digit Divisors /Enduring What is the standard procedure for division and why does it work? Basic facts and place-value patterns can be used to divide multiples of 10, 100 and so forth by one-digit numbers. The sharing interpretation of division and money can be used to model the standard division algorithm. There is more than one way to estimate a quotient. Substituting compatible numbers is an efficient technique for estimating quotients. Different numerical expressions can have the same value. 4.1 Dividing Multiples of 10 and Estimating Quotients 4.3 Reasonableness 4.4 Connecting Models & Symbols 4.5 Dividing by 1-Digit Divisors 4.6 Zeros in the Quotient 4.7 Draw a picture and Write an Equation

5 Suggested Blocks of Topic: Topic 5-Dividing by 2-digit Divisors Instruction: 10 days / November / Perform operations with multidigit whole numbers and with decimals to hundredths. 5.NBT.6. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. What is the standard procedure for dividing with two-digit divisors? Using basic facts and patterns can be helpful in dividing by multiples of 10. Using area models and arrays can help students understand the algorithm for dividing by 2-digit divisors. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. Patterns can sometimes be used to identify the relationship between quantities. There is more than one way to estimate a quotient. Substituting compatible numbers in as efficient technique for estimating quotients. Dividing by 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help determine the placement of digits in the quotient. Dividing with multi-digit divisors is just an extension of the steps for dividing with 1 and 2-digit divisors. Estimation and place value can help determine the placement of digits in the quotient. 5.1 Using Patterns to Divide 5.2 Estimating Quotients with 2-Digit Divisors 5.3 Connecting Models & Symbols 5.4 Dividing by Multiples of Digit Quotients Digit Quotients 5.7 Estimating & Dividing with Greater 5.8 Missing or Extra Information

6 Suggested Blocks of Instruction: 9 days / December Topic: Topic 6-Multiplying Decimals / Understand the place value system. 5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. Perform operations with multidigit whole numbers and with decimals to hundredths. 5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. What are the standard procedures for estimating and finding products involving decimals? Patterns can be used to mentally multiply decimals by 10, 100, and 1,000. Compare each factor to 1 as a way of determining if you have placed the decimal point reasonably. Rounding and compatible numbers can be used to estimate the product of a whole number and a decimal. The standard multiplication algorithm involving decimals is an extension of the standard algorithm for multiplying whole numbers. The steps for multiplying whole numbers by decimals are similar to the steps for multiplying two whole numbers. Place value determines the placement of the decimal point in a product. Steps for multiplying decimals are similar to steps for multiplying whole numbers. Place value determines the placement of the decimal point in a product. The product of two decimals less than one is less than either factor. Materials: 6nvision Math 6.1 Multiplying Decimals by 10,100 or 1, Estimating the Product of a Decimal and a Whole Number 6.3 Number Sense: Decimal Multiplication 6.4 Models for Multiplying Decimals 6.5 Multiplying a Decimal by a Whole # 6.6 Multiplying Two Decimals 6.7 Multiple-Step Problems

7 9 days / January Understand the place value system. 5.NBT.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Topic: Topic 7-Dividing Decimals /Enduring What are the standard procedures for estimating and finding quotients involving decimals? Place-value patterns can be used to mentally divide decimals by 10, 100, or 1,000. Estimating quotients for whole number divisors and dividends can be applied to calculations with decimal dividends and divisors. Substituting compatible numbers can be used in most cases. The location of decimal points in decimal division calculations can sometimes be decided by reasoning about the relative size of the given numbers. The standard division algorithm involving decimals is an extension of the standard algorithm for dividing whole numbers. A number divided by a decimal can be represented as an equivalent calculation using place value to change the divisor to a whole number. Materials: 7nvision Math 7.1 Dividing Decimals by 10, 100 or 1, Estimating Decimal Quotients 7.3 Number Sense: Decimal Divison 7.4 Dividing by a Whole Number 7.5 Dividing a Whole Number by a Decimal 7.6 Dividing a Decimal by a Decimal 7.7 Multiple-Step Problems

8 Suggested Blocks of Instruction: 11 days / January Topic: Topic 8-Numerical Expressions, Patterns, and Relationships. /Enduring Write and interpret numerical expressions. 5.OA.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Analyze patterns and relationships. 5.OA.3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. How are the values of an algebraic expression and a numerical expression found? Some mathematical phrases can be represented using a variable in an algebraic expression. There is an agreed upon order for which operations in a numerical expression are performed. To simplify a numerical expression, first compute within parentheses. Second, evaluate all terms with exponents. Then do any multiplications and division calculations from left to right followed by an addition and subtraction calculations from left to right. Patterns can sometimes be used to identify a relationship between two quantities. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. Patterns that repeat in predictable ways may be used to identify relationships. Some mathematical phrases can be represented using a variable in an algebraic expression. 8.1 Using Variables to Write Expressions 8.2 Order of Operations 8.3 Simplifying Expressions 8.4 Evaluating Expressions 8.5 Addition & Subtraction Expressions 8.6 Multiplication & Division Expressions 8.7 Patterns: Extending Tables 8.8 Variables & Expressions 8.9 Act It Out & Use Reasoning

9 Suggested Blocks of Instruction: 12 days/ January / February Objectives/CPI s/ Standards Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Topic: Topic 9- Adding and Subtracting Fractions / What does it mean to add and subtract fractions wit unlike denominators? What is a standard procedure for adding and subtracting fractions with unlike denominators? The same fractional amount can be represented by an infinite set of different but equivalent fractions. Equivalent fractions are found by multiplying or dividing the numerator and denominator by the same nonzero number. A fraction is in simplest form when 1 is the only common factor of the numerator and denominator. A number line can be sued to determine the nearest half or whole a fraction is closest to. All nonzero whole numbers have common multiples, including a least one. Sometimes the least common multiples of two numbers are one of the numbers. Fractions with unlike denominators can be added or subtracted by replacing fractions with equivalent fractions with like denominators. The product of the denominators of two fractions is a common denominator of both. Fraction sums and differences can be estimated by replacing fractions with the closest half or whole. 9.1 Equivalent Fractions 9.2 Fractions in Simplest Form 9.3 Writing to Explain 9.4 Estimating Sums & Differences of Fractions 9.5 Common Multiples& Least Common Multiple 9.6 Finding Common Denominators 9.7 Adding Fractions with Unlike Denominators 9.8 Subtracting Fractions with Unlike Denominators 9.9 More Adding & Subtracting Fractions 9.10 Draw a Picture and Write an Equation

10 Suggested Blocks of Instruction: 9 days / February / March Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators 5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Topic: Topic 10-Adding and Subtracting Mixed Numbers /Enduring What does it mean to add and subtract mixed numbers? What is a standard procedure for adding and subtracting mixed numbers? Fractional amounts greater than 1 can be represented using a whole number and a fraction. Whole number amounts can be represented as fractions. When the numerator and denominator are equal, the fraction equals 1. Fractions greater than 1 can be named using a whole number and a fraction or an improper fraction. Models can be used to show different ways of adding and subtracting mixed numbers. There is more than one way to add or subtract mixed numbers. Sums and differences of mixed numbers can be estimated by rounding each mixed number to the nearest whole number. One way to add mixed numbers is to utilize a number line to model and find common denominators. Sometimes whole numbers or fractions need to be renamed. One way to subtract mixed numbers is to utilize a number line model and find common denominators. Sometimes whole numbers or fractions need to be renamed Improper Fractions & Mixed Numbers 10.2 Estimating Sums & Differences of Mixed Numbers 10.3 Modeling Addition & Subtraction of Mixed Numbers 10.4 Adding Mixed Numbers 10.5 Subtracting Mixed Numbers 10.6 More Adding & Subtracting Mixed Numbers 10.7 Draw a Picture and Write an Equation

11 13 days / March Topic: Topic 11-Multiplying and Dividing Fractions and Mixed Numbers Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.3. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers whose answers contain fractions. 5.NF.4. Multiply a fraction or whole #by a fraction. 4a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. 5.NF.5. Interpret multiplication as scaling (resizing), by: 5a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor 5b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. 5.NF.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. 5.NF.7. Apply and extend previous understandings of division to divide unit fractions by whole # s and whole # s by unit fractions. 7a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) 4 = 1/12 because (1/12) 4 = 1/3. 7b. Interpret division of a whole number by a unit fraction 7c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. /Enduring What are the standard procedures for estimating and finding products and quotients of fractions and mixed numbers? A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole to be divided. The product of a hole number and a fraction can be interpreted in different ways. One interpretation is repeated addition. Multiplying a whole number by a fraction involves division as well as multiplication. The product is a fraction of the whole number. A unit square can be used to show the area meaning of faction multiplication. When you multiply two fractions that are bot less than 1, the product is smaller than either fraction. To multiply fractions, write the product of the numerators over the product of the denominators. The inverse relationship between multiplication and division can be used to divide with fractions. Rounding and compatible numbers can be used to estimate the product of fractions or mixed numbers. The relative size of the factors can be used to determine the relative size of the product. One way to find the product of mixed numbers is to change the calculation to an equivalent one involving improper fractions. One way to find the quotient of a whole number divided by a fraction is to multiply the whole number by the reciprocal of the fraction Fractions & Division 11.2 Multiplying Fractions & Whole # s 11.3 Estimating Products 11.4 Multiplying Two Fractions 11.5 Area of a Rectangle 11.6 Multiplying Mixed Numbers 11.7 Multiplication as Scaling 11.8 Multiple-Step Problems 11.9 Dividing Whole Numbers by Unit Fractions Dividing Unit Fractions by Non- Zero Whole Numbers Draw a Picture and Write an Equation

12 9 days / March / April Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.3. Recognize volume as an attribute of solid figures and understand concepts of volume measurement. 3a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. 3b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. 5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. 5b. Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. 5c.Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Topic: Topic 12-Volume of Solids /Enduring How can three-dimensional shapes be represented and analyzed? What does the volume of a rectangular prism mean and how can it be found? Three dimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces, edges, and vertices. Many everyday objects closely approximate standard geometric solids The shape of a solid can sometimes be determined by analyzing different views of the solid. Volume is a measure of the amount of space inside a solid figure. Volume can be measured by counting the number of cubic units needed to fill a three-dimensional object. The volume of some objects can be found by breaking apart the object into other objects for which the volume of each can be found Solids 12.2 View of Solids 12.3 Use Objects & Solve a Simpler Problem 12.4 Models & Volume 12.5 Volume 12.6 Combining Volumes 12.7 Use Objects & Reasoning

13 9 days / April Topic: Topic 13-Units of Measure Convert like measurement units within a given measurement system. 5.MD.1. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real world problems. /Enduring What are the customary measurement units and how are they related? What are metric measurement units and how are they related? Relationships between measurement units of the same length can be expressed as an equation (e.g., 1 ft = 12 in; 1 m = 100 cm). Relationships exist that enable you to convert between units of length by multiplying or dividing. Relationships between measurement units of the same capacity can be expressed as a ration (e.g., 1 qt to 2 pt or 1 qt = 1 pt; 1 L to 1,000 ml or 1 L = 1,000 ml). Relationships between measurement units of weight/mass can be expressed as ration (e.g., 1 lb to 16 oz or 1 lb = 16 oz; 1 kg to 1,000 g or 1 kg = 1,000 g) Converting Customary Units of Length 13.2 Converting Customary Units of Capacity 13.3 Converting Customary Units of Weight 13.4 Converting Metric Units of Length 13.5 Converting Metric Units of Capacity 13.6 Converting Metric Units of Mass 13.7 Multiple-Step Problems

14 7 days / April / May Represent and interpret data. 5.MD.2. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Graph points on the coordinate plane to solve real-world and mathematical problems. 5.G.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Topic: Topic 14-Data /Enduring How can line plots be used to represent data and answer questions? How can numbers be used to describe certain data sets? Each type of graph is most appropriate for certain kinds of data. A line plot organizes data on a number line and is useful for showing visually how a set of data is distributed. Some questions can be answered using a survey. An appropriately selected sample can be sued to make predictions about a population. Sample size is one factor that determines how close data from the same will mirror the population Line Plots 14.2 Data from Surveys 14.3 Making Line Plots 14.4 Measure Data 14.5 Writing to Explain

15 8 days (May to June) Classify two-dimensional figures into categories based on their properties. 5.G.3. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. 5.G.4. Classify two-dimensional figures in a hierarchy based on properties Topic: Topic 15 Classifying Plane Figures /Enduring How can angles be measured and classified? How can polygons, triangles, and quadrilaterals be described, classified, and named? Plane shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles. Classify two-dimensional shapes into categories based on their properties Polygons 15.2 Triangles 15.3 Properties of Quadrilaterals 15.4 Special Quadrilaterals 15.5 Classifying Quadrilaterals 15.6 Make & Test Generalizations

16 8 days / May / June Graph points on the coordinate plane to solve real-world and mathematical problems. 5.G.1. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x- axis and x-coordinate, y-axis and y-coordinate). 5.G.2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Topic: Topic 16-Coordinate Geometry /Enduring How are points graphed? How can we show the relationship between sequences on a graph? The coordinate system is a scheme that uses two perpendicular lines intersecting at 0 to name the location of points in the plane. A graph of a rule contains all of the points on the coordinate grid whose x and y coordinates satisfy the rule. Mathematical relationships represented by rules can also be represented by a graph of the rule. Ordered pairs that satisfy the rule can be sued to graph the data Ordered Pairs 16.2 Distances on a Coordinate Plane 16.3 Solve a Simpler Problem 16.4 Patterns & Graphing 16.5 More Patterns & Graphing 16.6 Work Backward